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Summer 2002
IMA Hot Topics Workshop
Numerical Relativity
June 24-29, 2002


Jointly sponsored with the Center for Gravitational Wave Physics, Penn State

Organizers:

Douglas N. Arnold Institute for Mathematics and its Applications arnold@ima.umn.edu
Abhay Ashtekar Center for Gravitational Wave Physics, Penn State ashtekar@gravity.phys.psu.edu
Pablo Laguna Center for Gravitational Wave Physics, Penn State pablo@astro.psu.edu

 

Description:

The numerical solution of Einstein's equations of general relativity promises to become one of the most potent tools for for understanding the complex behavior of strong dynamical gravitational fields. In recent years the field of numerical relativity has grown substantially, engaging the efforts of large groups of researchers across the globe. Despite some promising results, the development of accurate, efficient, and validated algorithms for Einstein's equations remains elusive. This is in part due to the size and complexity of the equations, but also due to fundamental issues which remain to be fully understood.

The problems of numerical relativity share many features with other large scale problems of computational physics, and it is highly likely that lessons learned in fields such as computational fluid dynamics, solid mechanics, and electromagnetics will help advance numerical relativity. But the fundamental differences between general relativity and classical field theories also bring major new computational issues.

This workshop will bring together numerical relativists and mathematicians working in fields such as numerical analysis, scientific computation, partial differential equations, and geometry, for an intense but informal period aimed at maximal communication and interaction between diverse researchers. The primary goals are to bring new ideas and techniques into the numerical relativity community and to propel applied mathematicians with relevant skills and interests into NR. We hope that this workshop will lead to continued interactions which could take place at many venues such as the Center for Gravitational Wave Physics at Penn State, the Institute for Theoretical Physics at UC Santa Barbara, the Caltech Visitors Program in the Numerical Simulation of Gravitational Wave Sources, and the IMA. Such interactions can lay the foundation for the formation of multidisciplinary teams better equipped to tackle the challenges of numerical relativity.

The workshop will focus on a few of the many issues in numerical relativity, selected for their importance, mathematical nature, and relative accessibility. Main among these are the initial value problem of vacuum relativity, including the encoding as partial differential equations; discretization techniques for these equations; treatment of black hole spacetimes; the imposition of boundary conditions; and the determination of physically relevant initial data.

WORKSHOP SCHEDULE

Monday Tuesday Saturday
MONDAY, JUNE 24
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Introduction to GR for computational scientists, with an emphasis on the vacuum field equations and issues like geometric well-posedness; PDE formulations; initial value problems; gauge freedom, etc. This will be most directed at the participants who have not had much to do with GR in the past, but will also serve to set a common vocabulary for the remainder of the week. The day will end with a reception at which all participants are invited to display posters.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

9:00 am Douglas Arnold, Fadil Santosa, and Lee Samuel Finn Welcome and Introduction
9:10-10:00 am Douglas N. Arnold

A quick introduction to the Einstein equations

notes (pdf    ps)

Slides.pdf

10:00-10:30 am Discussion  
10:30-11:00 am Break Reception Room EE/CS 3-176
11:00-11:50 am Alan D. Rendall
Albert-Einstein-Institut

Introduction to GR for computational scientists, II

notes (pdf    ps)

11:50 am-12:30 pm Discussion  
12:30-2:30 pm
Break
 
2:30-3:20 pm Robert Bartnik
University of Canberra

Introduction to the 3+1 Einstein equations

notes (pdf    ps)

3:20-4:00 pm Discussion  
4:00-6:00 pm Reception and Posters IMA East, 400 Lind Hall
TUESDAY, JUNE 25
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The morning will focus on key ideas from better developed areas of computational science: electromagnetics and hyperbolic systems from other applications. The afternoon will focus on formulations of GR for computation.
8:30 am Coffee Reception Room EE/CS 3-176
9:00-9:50 am Ralf Hiptmair
IAM, Universitaet Bonn

Discretization of Maxwell's Equations (pdf    ps)

slides.pdf    slides.ps

9:50-10:30 am Discussion  
10:30-11:00 am Break Reception Room EE/CS 3-176
11:00-11:50 am Eitan Tadmor
University of California Los Angeles
Computational Methods for Hyperbolic Systems. Preservation of Global and Local Invariants  (pdf)
11:50 am-12:30 pm Discussion  
12:30-2:30 pm
Break
 
2:30-3:00 pm Oscar Reula
FaMAF, Universidad Nacional de Cordoba

Formulations of GR for computation, I

slides.pdf

3:00- 3:30 pm Discussion  
3:30-3:45 pm Break Reception Room EE/CS 3-176
3:45-4:15 pm Manuel Tiglio
Louisiana State University

Numerical relativity as an initial-boundary value problem

slides.pdf

4:15-4:45 pm Discussion  
WEDNESDAY, JUNE 26
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The morning will extend the tutorials of the first day to issues involving black holes and horizons. The remaining talks will focus on the main conceptual and numerical challenges in numerical relativity. During dinner there will be the possibility for any participants with relevant software and computations to demonstrate to do so.
8:30 am Coffee Reception Room EE/CS 3-176
9:00-9:50 am Jeff Winicour
University of Pittsburgh

Black hole spacetimes   slides.html

notes (ps)

9:50-10:30 am Discussion  
10:30-11:00 am Break Reception Room EE/CS 3-176
11:00-11:50 am Matthew W. Choptuik
University of British Columbia

Fundamental issues of numerical relativity

slides.html    slides.pdf    slides.ppt

11:50 am-12:30 pm Discussion  
12:30-2:30 pm
Break
 
2:30-3:20 pm Pablo Laguna
Penn State University

State of the art of numerical relativity

slides.pdf

3:20-4:00 pm Discussion  
5:30-8:00 pm Pizza Dinner/Computational Demonstrations, Lind Hall 409

The following brief presentations will be given:
Jeff Winicour Well-posed initial-boundary evolutions
Jinchao Xu Problem-independent adaptivity and multigrid
Michael J. Holst MC, Manifold Code
Robert Bartnik Null quasispherical numerical evolution
Denis Pollney Gauges in the BSSN formulation of GR
THURSDAY, JUNE 27
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The day will focus on some particular challenges and promising techniques for numerical relativity.
8:30 am Coffee Reception Room EE/CS 3-176
9:00-9:30 am Gregory B. Cook
Wake Forest University

Computation of initial data, I

slides

9:30-9:50 am Discussion  
9:50-10:05 am Break Reception Room EE/CS 3-176
10:05-10:35 am Michael J. Holst
University of California, San Diego

Computation of initial data, II

slides.pdf

10:35-10:55 am Discussion  
10:55-11:10 am Break Reception Room EE/CS 3-176
11:10 am-11:25 pm Markus Keel
University of Minnesota

Linear degeneracy of the Einstein

Slides

11:25-11:40 am Discussion  
11:40-11:55 am Eitan Tadmor
University of California Los Angeles
Remarks on first order formulations
11:55 am -12:10 pm Discussion  
12:10-2:30 pm Break  
2:30- 3:00 pm Deirdre Shoemaker
Penn State University

Computation of horizons and excision

slides.pdf

3:00-3:30 pm Discussion  
3:30-3:45 pm Break Reception Room EE/CS 3-176
3:45-4:15 pm Mark A. Scheel
California Institute of Technology

Spectral methods and excision

slides.pdf

4:15- 4:45 pm Discussion  
FRIDAY, JUNE 28
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The day will again focus on some particular challenges facing numerical relativity and promising techniques.
8:30 am Coffee Reception Room EE/CS 3-176
9:00-9:50 am Luis Lehner
University of British Columbia
Outer boundary conditions
9:50-10:30 am Discussion  
9:50-10:05 am Break Reception Room EE/CS 3-176
10:05-10:35 am Richard S. Falk
Rutgers University

Overview of finite element methods for linear hyperbolic problems

slides.pdf    slides.ps

10:35-10:55 am Discussion  
10:55-11:10 am Break Reception Room EE/CS 3-176
11:10-11:25 am Lee Lindblom
Caltech
Energy norms and stability of the Einstein equations
11:25 am-11:40 pm Discussion  
11:40-11:55 am Sasha Husa
Albert-Einstein-Institut

The conformal approach

slides.pdf

11:55 am-12:10 pm Discussion  
12:10-2:00 pm Lee Samuel Finn
Penn State University and
Lee Lindblom
Caltech

Lunchtime discussion on gravitational wave phenomenology
Lind Hall 409. Lunch will be provided.

GWPhenomIMA-slides.pdf
LIGOMath-slides.pdf

2:00- 4:00 pm Panel discussion on numerical methods
4:00- 4:15 pm Break Reception Room EE/CS 3-176
4:15- 4:30 pm Discussion  
6:15 pm Workshop Dinner
Radisson shuttle to Kikugawa at 6:00 pm
Kikugawa Restaurant
43 Main Street S.E., Minneapolis
SATURDAY, JUNE 29
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
The workshop will conclude with discussions and summary presentations assessing what was learned and future directions.
9:00-10:30 am

Discussion lead by Richard Price (University of Utah), Ragnar Winther (University of Oslo) and Beverly Berger (NSF)

Richard Price slides.html

10:30-11:00 pm Break
11:00 am -12:30 pm Discussion, continued
The workshop will end at 12:30 pm on Saturday.
Monday Tuesday Saturday

LIST OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)

As of 6/28/2002
Name Department Affiliation
Douglas N. Arnold   Institute for Mathematics and its Applications
Robert Bartnik Mathematics and Statistics University of Canberra
Beverly Berger Division of Physics National Science Foundation
David Brown Physics North Carolina State University
Matt Choptuik Physics University of British Columbia
Gregory B. Cook Physics Wake Forest University
Rick Falk Mathematics Rutgers University
Lee Samuel Finn Director, Center for Gravitational Wave Physics Penn State University
Jörg Frauendiener Theoretische Astrophysik Universität Tübingen
Ralf Hiptmair Mathematics University of Tübingen
Michael Holst Mathematics UC San Diego
Sascha Husa Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut
Marcus Keel Mathematics University of Minnesota
Pablo Laguna Center for Gravitational Wave Physics Penn State University
Luis Lehner Physics & Astronomy University of British Columbia
Lee Lindblom Physics, Math & Astronomy Caltech
Peter Monk Mathematical Sciences University of Delaware
Arup Mukherjee Mathematics Sciences Montclair State University
Denis Pollney Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut
Richard Price Physics University of Utah
Alan Rendall Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut
Oscar Reula Investigador Independiente, CONICET FaMAF, Universidad Nacional de Cordoba
Mark A. Scheel Physics, Mathematics, and Astronomy California Institute of Technology
Deirdre Shoemaker Astronomy Penn State University
Eitan Tadmor Mathematics University of California Los Angeles
Blake Temple Mathematics University of California
Manuel Tiglio Physics Louisiana State University
Jeff Winicour Physics University of Pittsburgh
Ragnar Winther Informatics University of Oslo
Jinchao Xu Mathematics Pennsylvania State University

 

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